Influence of dose per fraction and alpha/beta ratio on the variation in biological effectiveness caused by physical dose inhomogeneity

Successful radiotherapy requires delivery of a tumoricidal treatment while sparing as much normal tissue as possible in the target volume. The aim of optimizing radiation treatment planning is to satisfy this requirement whilst achieving a homogeneous dose distribution with in the target volume. However, expressing the treatment plan solely as a physical dose distribution might be misleading. In the most centres variation of 0% [ +/- 5%], or even more, is considered to be an acceptable range of inhomogeneity. If we convert isodose lines [phsical dose distribution] in an irradiated volume into isoeffect lines [biological effect distribution], using the linear quadratic model, the inhomogeneity factor will be increased. In this analysis an equation has been introduced to calculate the biological dose inhomogeneity factor in terms of the physical dose inhomogeneity. The biological inhomogeneity factor depends on the fraction size as well as radiobiology of the irradiated tissue [e.g. alpha/beta ratio]. The biological dose inhomogeneity factor depends on the fraction size as well as radiobiology of the irradiated tissue [e.g. alpha/beta ratio]. The biological dose inhomogeneity factor resulting in a 10% physical dose inhomogeneity was calculated for isoeffective schedules with different fraction size [1-5 GY]. For late responding tissues with alpha/beta of 1 to 5 GY, the biological inhomogeneity ranged from 12% [ +/- 6%] to 19% [ +/- 9.5%] depending a/B and fraction size. For tumours and actue responding tissues with alpha/beta values ranging between 5 and 20 Gy, the biological dose inhomogeneity was between 11% [ +/- 5.5%] and 15% [ +/- 7.5%]. For late responding tissues an increase of 9.5% in the biological effective dose may give a significant increase in the complication probability. Also a reduction of the effective dose by 7.5% may give a substantial drop in the tumour curability. Therefore, it may be useful to express the outcome of radiotherapy treatment planning in terms of calculated biological effect distribution as well as distribution of physical dose. The analysis shows that hyperfractionated schedules generate lesser biological dose inhomogeneity for any given level of physical dose inhomogeneity. This spatial consideration provide an additional rationale for use of hyperfractionated treatment scheduled in radiotherapy